I am so rusty, I need help solving these problems. I attempted some and i have my attempted solutions at the end of each question. However, im not sure about them. Can anyone show me step by step solutions to these? Can anyone help please? It is so URGENT!!! I'd greatly appreciate it. Thanks

1: 200 internet connections were tested for their quality of service

(number of packets dropped) and speed (high and low). The data is as shown:

High Quality Low Quality

High Speed 140 18

Low Speed 32 10

If we define A={a connection is of high quality}, B={a connection has high speed}

find P(A), P(B) and P(A and B) and determine if A and B are independent events.

My attempt

P(A) = (140 +32)/200

P(B) = (140 +18)/200

P(A n B) = the product of the two

2: In an 8 bit word each bit is equally likely to be 0 or 1.

(a) Find the probability that all bits are 1's.

(b) Find the probability that all bits are 0's.

(c) Find the probability that exactly 1 bit is 1 and 7 bits are 0's.

My Attempt

(a)8/256

(b)8/256

3: In a packet switched network there are two types of routes: congested

and not congested. Assume that 30% of the routes are congested.

The probability of a dropped packet is 0.001 when the connection is not

congested, and the probability is 0.01 when the connection is congested.

(a) Find the probability that a packet is dropped.

(b) If a packet is dropped what is the probability that it was sent on

a congested route?